Cooling with a Shaped Pin Fin
Cooling with a Shaped Pin Fin
In electronic systems, a fin is a heat sink (passive heat exchanger) that cools a device by dissipating heat to the surrounding medium (e.g. air). Such a pin fin is used to maximize heat transfer to a fluid between two walls.
A pin fin has an elliptical external surface, as shown in the "pin fin image".
The walls are at a high temperature . The fluid flowing over the pin has a free stream temperature . The coefficient of heat transfer between the pin wall and the surrounding medium is labeled (in ). If one introduces the dimensionless temperature
T
w
T
∞
h
W/K
2
m
ϕ=-
T-
T
∞
T
w
T
∞
1
r
∂
∂r
∂ϕ
∂r
2
∂
∂
2
z
The associated boundary conditions are then:
∂ϕ
∂z
z=0
∂ϕ
∂r
r=0
∂ϕ
∂r
h
k
r=(z)
r
0
ϕ(z=L)==1
ϕ
w
where is the thermal conductivity of the cylindrical pin fin and (z)=1-α.
k (W/m K)
r
0
1-
2
z
This Demonstration plots the contours of the dimensionless temperature for a user-set value of the Biot number and the shape factor .
Bi=
h(1)
r
0
k
α